A lower bound for disconnection by random interlacements. (English) Zbl 1355.60035

Li, Xinyi; Sznitman, Alain-Sol

Electron. J. Probab. 19, Paper No. 17, 26 p. (2014).

Summary: We consider the vacant set of random interlacements on \(\mathbb{Z}^d\), with \(d\) bigger or equal to 3, in the percolative regime. Motivated by the large deviation principles obtained in our recent work [Probab. Theory Relat. Fields 161, No. 1–2, 309–350 (2015; Zbl 1314.60078)], we investigate the asymptotic behavior of the probability that a large body gets disconnected from infinity by the random interlacements. We derive an asymptotic lower bound, which brings into play tilted interlacements, and relates the problem to some of the large deviations of the occupation-time profile considered in [loc. cit.].

MSC:

60F10	Large deviations
60K35	Interacting random processes; statistical mechanics type models; percolation theory
60J27	Continuous-time Markov processes on discrete state spaces

Keywords:

random interlacements; disconnection; large deviations

Citations:

Zbl 1314.60078